Focal-plane Wavefront Sensing for Active Optics in the VST Based on an Analytical Optical Aberration Model R.Holzl¨ohner a , S. Taubenberger a , A. P. Rakich b,a , L. Noethe a , P. Schipani c and K. Kuijken d a European Southern Observatory (ESO), Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany; b GMTO Corp., Pasadena, CA 91107, USA; c INAF - Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131 Naples, Italy; d Leiden Observatory, Niels Bohrweg 2, NL-2333 CA Leiden, Netherlands ABSTRACT We study a novel focal plane wavefront sensing and active optics control scheme at the VST on Cerro Paranal, an f/5.5 survey telescope with a 1 1 degree field of view and a 2.6 m primary mirror. This scheme analyzes the elongation pattern of stellar PSFs across the full science image (256 Mpixels) and compares their second moments with an analytical model based on 5th-order geometrical optics. We consider 11 scalar degrees of freedom in mirror misalignments and deformations (M2 piston, tip/tilt and lateral displacement, detector tip/tilt, plus M1 figure astigmatism and trefoil). Using a numerical optimization method, we extract up to 4000 stars and complete the fitting process in under one minute. We demonstrate successful closed-loop active optics control based on maximum likelihood filtering. Keywords: active optics, wide-field telescopes, point spread function, elongation, aberration, optical plate diagram 1. INTRODUCTION Active optics is essential in modern large telescopes to compensate mirror misalignments and misfigure, mostly caused by temperature and gravity vector variations. 1, 2 Closed-loop active optics control of wide-field telescopes is demanding both because of the tight alignment tolerances in fast optics, and also because the field dependence of aberrations in misaligned wide-field systems places tighter constraints on various system degrees of freedom than is the case with more conventional narrow field-of-view telescopes. On the other hand, wide-field telescopes are often employed to run surveys, some of which require good PSF uniformity across the field and high overall image quality, in particular dark matter surveys such as KiDS. 3, 4 Wide-field telescopes often rely on curvature wavefront sensing (CWFS) to feed their active optics systems, which analyzes highly defocused star images(”donuts”), typically on the edge of the science field. However, since CWFS senses irradiance variations in the pupil induced by the second derivatives of the wavefront, the measurement errors in the low-order aberrations are higher than in Shack-Hartmann or pyramid wavefront sensors under identical conditions. 5 Moreover, CWFS can only sample a few points in the field and thus it may be advantageous to validate (and improve upon) their performance using a complimentary wavefront sensing scheme. In this article, we continue a study of the ellipticity method, a focal plane wavefront sensing scheme without the need for additional sensor hardware. 6, 7 This method solely uses science images (in the case of the VST, provided by the 256-Mpix visible light camera OmegaCAM 8 ), extracts up to 4000 stars uniformly covering the entire field, and analyzes the second moments of their PSFs. The resulting pattern of PSF sizes and ellipticities is then compared with the pattern from an analytical model, based on 5th-order geometrical optics. This model expresses the star PSF second moments for the misaligned telescope with shape distortions in the primary mirror. The Levenberg-Marquardt multidimensional minimization method 9 is then applied to rapidly approximate the observation. Further author information: (Send correspondence to R.H. E-mail: rholzloe at eso.org, Tel. +49 89 3200 6671, www.eso.org)